Read Ebook: A Treatise on Mechanics by Kater Henry Lardner Dionysius

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Ebook has 910 lines and 130412 words, and 19 pages

PROPERTIES OF MATTER.

Organs of Sense.--Sensations.--Properties or Qualities.--Observation. --Comparison and Generalisation.--Particular and general Qualities.-- Magnitude.--Size.--Volume.--Lines.--Surfaces.--Edges.--Area.--Length. --Impenetrability.--Apparent Penetration.--Figure.--Different from Volume.--Atoms.--Molecules.--Matter separable.--Particles.--Force.-- Cohesion of Atoms.--Hypothetical Phrases unnecessary.--Attraction. 1

PROPERTIES OF MATTER, CONTINUED.

Divisibility.--Unlimited Divisibility.--Wollaston's micrometric Wire. --Method of making it.--Thickness of a Soap Bubble.--Wings of Insects. --Gilding of Wire for Embroidery.--Globules of the Blood.-- Animalcules.--Their minute Organisation.--Ultimate Atoms.--Crystals.-- Porosity.--Volume.--Density.--Quicksilver passing through Pores of Wood.--Filtration.--Porosity of Hydrophane.--Compressibility.-- Elasticity.--Dilatability.--Heat.--Contraction of Metal used to restore the Perpendicular to Walls of a Building.--Impenetrability of Air.--Compressibility of it.--Elasticity of it.--Liquids not absolutely incompressible.--Experiments.--Elasticity of Fluids.-- Aeriform Fluids.--Domestic Fire Box.--Evolution of Heat by compressed Air. 9

INERTIA.

Inertia.--Matter Incapable of spontaneous Change.--Impediments to Motion.--Motion of the Solar System.--Law of Nature.--Language used to express Inertia sometimes faulty.--Familiar Examples of Inertia. 27

ACTION AND REACTION.

Inertia in a single Body.--Consequences of Inertia in two or more Bodies.--Examples.--Effects of Impact.--Motion not estimated by Speed or Velocity alone.--Examples.--Rule for estimating the Quantity of Motion.--Action and Reaction.--Examples of.--Velocity of two Bodies after Impact.--Rule for finding the common Velocity after Impact.--Magnet and Iron.--Feather and Cannon Ball impinging. --Newton's Laws of Motion.--Inutility of.--Familiar Effects resulting from Consequences of Inertia. 34

COMPOSITION AND RESOLUTION OF FORCE.

ATTRACTION.

Impulse.--Mechanical State of Bodies.--Absolute Rest.--Uniform and rectilinear Motion.--Attractions.--Molecular or atomic.--Interstitial Spaces in Bodies.--Repulsion and Attraction.--Cohesion.--In Solids and Fluids.--Manufacture of Shot.--Capillary Attractions.--Shortening of Rope by Moisture.--Suspension of Liquids in capillary Tubes.-- Capillary Siphon.--Affinity between Quicksilver and Gold.--Examples of Affinity.--Sulphuric Acid and Water.--Oxygen and Hydrogen.--Oxygen and Quicksilver.--Magnetism.--Electricity and Electro-Magnetism.-- Gravitation.--Its Law.--Examples of.--Depends on the Mass.-- Attraction between the Earth and detached Bodies on its Surface.-- Weight.--Gravitation of the Earth.--Illustrated by Projectiles.-- Plumb-Line.--Cavendish's Experiments. 63

TERRESTRIAL GRAVITY.

Phenomena of falling Bodies.--Gravity greater at the Poles than Equator.--Heavy and light Bodies fall with equal Speed to the Earth. --Experiment.--Increased Velocity of falling Bodies.--Principles of uniformly accelerated Motion.--Relations between the Height, Time, and Velocity.--Attwood's Machine.--Retarded Motion. 84

OF THE MOTION OF BODIES ON INCLINED PLANES AND CURVES.

Force perpendicular to a Plane.--Oblique Force.--Inclined Plane.-- Weight produces Pressure and Motion.--Motion uniformly accelerated.-- Space moved through in a given Time.--Increased Elevation produces increased Force.--Perpendicular and horizontal Plane.--Final Velocity.--Motion down a Curve.--Depends upon Velocity and Curvature. --Centrifugal Force.--Circle of Curvature.--Radius of Curvature.-- Whirling Table.--Experiments.--Solar System.--Examples of centrifugal Force. 85

THE CENTRE OF GRAVITY.

Terrestrial Attraction the combined Action of parallel Forces.-- Single equivalent Force.--Examples.--Method of finding the Centre of Gravity.--Line of Direction.--Globe.--Oblate Spheroid.--Prolate Spheroid.--Cube.--Straight Wand.--Flat Plate.--Triangular Plate.-- Centre of Gravity not always within the Body.--A Ring.--Experiments. --Stable, instable, and neutral Equilibrium.--Motion and Position of the Arms and Feet.--Effect of the Knee-Joint.--Positions of a Dancer. --Porter under a Load.--Motion of a Quadruped.--Rope Dancing.-- Centre of Gravity of two Bodies separated from each other.-- Mathematical and experimental Examples.--The Conservation of the Motion of the Centre of Gravity.--Solar System.--Centre of Gravity sometimes called Centre of Inertia. 107

An Axis.--Planets and common spinning Top.--Oscillation or Vibration. --Instantaneous and continued Forces.--Percussion.--Continued Force. --Rotation.--Impressed Forces.--Properties of a fixed Axis.--Movement of the Force round the Axis.--Leverage of the Force.--Impulse perpendicular to, but not crossing, the Axis.--Radius of Gyration.-- Centre of Gyration.--Moment of Inertia.--Principal Axes.--Centre of Percussion. 128

OF THE PENDULUM.

Isochronism.--Experiments.--Simple Pendulum.--Examples illustrative of.--Length of.--Experiments of Kater, Biot, Sabine, and others.-- Huygens' Cycloidal Pendulum. 145

OF SIMPLE MACHINES.

Statics.--Dynamics.--Force.--Power.--Weight.--Lever.--Cord.-- Inclined Plane. 160

OF THE LEVER.

Arms.--Fulcrum.--Three Kinds of Levers.--Crow Bar.--Handspike.--Oar. --Nutcrackers.--Turning Lathe.--Steelyard.--Rectangular Lever.-- Hammer.--Load between two Bearers.--Combination of Levers.-- Equivalent Lever. 167

OF WHEEL-WORK.

Wheel and Axle.--Thickness of the Rope.--Ways of applying the Power. --Projecting Pins.--Windlass.--Winch.--Axle.--Horizontal Wheel.-- Tread-Mill.--Cranes.--Water-Wheels.--Paddle-Wheel.--Rachet-Wheel.-- Rack.--Spring of a Watch.--Fusee.--Straps or Cords.--Examples of.-- Turning Lathe.--Revolving Shafts.--Spinning Machinery.--Saw-Mill.-- Pinion.--Leaves.--Crane.--Spur-Wheels.--Crown-Wheels.--Bevelled Wheels.--Hunting-Cog.--Chronometers.--Hair-Spring.--Balance-Wheel. 178

OF THE PULLEY.

Cord.--Sheave.--Fixed Pulley.--Fire Escapes.--Single moveable Pulley.--Systems of Pulleys.--Smeaton's Tackle.--White's Pulley.-- Advantage of.--Runner.--Spanish Bartons. 199

ON THE INCLINED PLANE, WEDGE, AND SCREW.

Inclined Plane.--Effect of a Weight on.--Power of.--Roads.--Power Oblique to the Plane.--Plane sometimes moves under the Weight.-- Wedge.--Sometimes formed of two inclined Planes.--More powerful as its Angle is acute.--Where used.--Limits to the Angle.--Screw. --Hunter's Screw.--Examples.--Micrometer Screw. 209

ON THE REGULATION AND ACCUMULATION OF FORCE.

Uniformity of Operation.--Irregularity of prime Mover.--Water-Mill. --Wind-Mill.--Steam Pressure.--Animal Power.--Spring.--Regulators. --Steam-Engine.--Governor.--Self-acting Damper.--Tachometer.-- Accumulation of Power.--Examples.--Hammer.--Flail.--Bow-string.-- Fire Arms.--Air-Gun.--Steam-Gun.--Inert Matter a Magazine for Force.--Fly-Wheel.--Condensed Air.--Rolling Metal.--Coining-Press. 224

MECHANICAL CONTRIVANCES FOR MODIFYING MOTION.

Division of Motion into rectilinear and rotatory.--Continued and reciprocating.--Examples.--Flowing Water.--Wind.--Animal Motion.-- Falling of a Body.--Syringe-Pump.--Hammer.--Steam-Engine.--Fulling Mill.--Rose-Engine.--Apparatus of Zureda.--Leupold's Application of it.--Hooke's universal Joint.--Circular and alternate Motion.-- Examples.--Watt's Methods of connecting the Motion of the Piston with that of the Beam.--Parallel Motion. 245

OF FRICTION AND THE RIGIDITY OF CORDAGE.

Friction and Rigidity.--Laws of Friction.--Rigidity of Cordage.-- Strength of Materials.--Resistance from Friction.--Independent of the Magnitude of Surfaces.--Examples.--Vince's Experiments.--Effect of Velocity.--Means for diminishing Friction.--Friction Wheels.-- Angle of Repose.--Best Angle of Draught.--Rail-Roads.--Stiffness of Ropes. 260

ON THE STRENGTH OF MATERIALS.

Difficulty of determining the Laws which govern the Strength of Materials.--Forces tending to separate the Parts of a Solid.--Laws by which Solids resist Compression.--Euler's theory.--Transverse Strength of Solids.--Strength diminished by the Increase of Height. --Lateral or Transverse Strain.--Limits of Magnitude.--Relative Strength of small Animals greater than large ones. 272

ON BALANCES AND PENDULUMS.

Weight.--Time.--The Balance.--Fulcrum.--Centre of Gravity of.-- Sensibility of.--Positions of the Fulcrum.--Beam variously constructed.--Troughton's Balance.--Robinson's Balance.--Kater's Balance.--Method of adjusting a Balance.--Use of it.--Precautions necessary.--Of Weights.--Adjustment of.--Dr. Black's Balance.-- Steelyard.--Roman Statera or Steelyard.--Convenience of.--C. Paul's Steelyard.--Chinese Steelyard.--Danish Balance.--Bent Lever Balance. --Brady's Balance.--Weighing Machine for Turnpike Roads.--Instruments for Weighing by means of a Spring.--Spring Steelyard.--Salter's Spring Balance.--Marriott's Dial Weighing Machine.--Dynamometer.-- Compensation Pendulums.--Barton's Gridiron Pendulum.--Table of linear Expansion.--Second Table.--Harrison's Pendulum.--Troughton's Pendulum.--Benzenberg's Pendulum.--Ward's Compensation Pendulum.-- Compensation Tube of Julien le Roy.--Deparcieux's Compensation.-- Kater's Pendulum.--Reed's Pendulum.--Ellicott's Pendulum.--Mercurial Pendulum.--Graham's Pendulum.--Compensation Pendulum of Wood and Lead.--Smeaton's Pendulum.--Brown's Mode of Adjustment. 278

THE

ELEMENTS OF MECHANICS.

PROPERTIES OF MATTER--MAGNITUDE--IMPENETRABILITY--FIGURE--FORCE.

Placed in the material world, Man is continually exposed to the action of an infinite variety of objects by which he is surrounded. The body, to which the thinking and living principles have been united, is an apparatus exquisitely contrived to receive and to transmit impressions. Its various parts are organised with obvious reference to the several external agents by which it is to be effected. Each organ is designed to convey to the mind immediate notice of some peculiar action, and is accordingly endued with a corresponding susceptibility. This adaptation of such organs to the particular influences of material agents, is rendered still more conspicuous when we consider that, however delicate its structure, each organ is wholly insensible to every influence except that to which it appears to be specially appropriated. The eye, so intensely susceptible of impressions from light, is not at all affected by those of sound; while the fine mechanism of the ear, so sensitively alive to every effect of the latter class, is altogether insensible to the former. The splendour of excessive light may occasion blindness, and deafness may result from the roar of a cannonade; but neither the sight nor the hearing can be injured by the most extreme action of that principle which is designed to affect the other.

To ascertain by observation the properties of bodies, is the first step towards obtaining a knowledge of nature. Hence man becomes a natural philosopher the moment he begins to feel and to perceive. The first stage of life is a state of constant and curious excitement. Observation and attention, ever awake, are engaged upon a succession of objects new and wonderful. The large repository of the memory is opened, and every hour pours into it unbounded stores of natural facts and appearances, the rich materials of future knowledge. The keen appetite for discovery implanted in the mind for the highest ends, continually stimulated by the presence of what is novel, renders torpid every other faculty, and the powers of reflection and comparison are lost in the incessant activity and unexhausted vigour of observation. After a season, however, the more ordinary classes of phenomena cease to excite by their novelty. Attention is drawn from the discovery of what is new, to the examination of what is familiar. From the external world the mind turns in upon itself, and the feverish astonishment of childhood gives place to the more calm contemplation of incipient maturity. The vast and heterogeneous mass of phenomena collected by past experience is brought under review. The great work of comparison begins. Memory produces her stores, and reason arranges them. Then succeed those first attempts at generalisation which mark the dawn of science in the mind.

To compare, to classify, to generalise, seem to be instinctive propensities peculiar to man. They separate him from inferior animals by a wide chasm. It is to these powers that all the higher mental attributes may be traced, and it is from their right application that all progress in science must arise. Without these powers, the phenomena of nature would continue a confused heap of crude facts, with which the memory might be loaded, but from which the intellect would derive no advantage. Comparison and generalisation are the great digestive organs of the mind, by which only nutrition can be extracted from this mass of intellectual food, and without which, observation the most extensive, and attention the most unremitting, can be productive of no real or useful advancement in knowledge.

The influence which forces have upon the form, state, arrangement, and motions of material substances is the principal object of physical science. In its strict sense, MECHANICS is a term of very extensive signification. According to the more popular usage, however, it has been generally applied to that part of physical science which includes the investigation of the phenomena of motion and rest, pressure and other effects developed by the mutual action of solid masses. The consideration of similar phenomena, exhibited in bodies of the liquid form, is consigned to HYDROSTATICS, and that of aeriform fluids to PNEUMATICS.

DIVISIBILITY--POROSITY--DENSITY--COMPRESSIBILITY--ELASTICITY--DILATABILITY.

Besides the qualities of magnitude and impenetrability, there are several other general properties of bodies contemplated in mechanical philosophy, and to which we shall have frequent occasion to refer. Those which we shall notice in the present chapter are,

Newton succeeded in determining the thickness of very thin laminae of transparent substances by observing the colours which they reflect. A soap bubble is a thin shell of water, and is observed to reflect different colours from different parts of its surface. Immediately before the bubble bursts, a black spot may be observed near the top. At this part the thickness has been proved not to exceed the 2,500,000th of an inch.

The transparent wings of certain insects are so attenuated in their structure that 50,000 of them placed over each other would not form a pile a quarter of an inch in height.

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